How do I mow the steep hill?

Instead of using a power mower I would first trim it with a weed-whacker. The danger of a mower on such a steep slope is very real--even a push mower is going to be tough. The alternative is not to mow it at all. Let the wildflowers and grass grow. it's good for the environment. 

They make tractors designed to mow across hills like highway ditches.  Obviously you can face the tractor down the hill and mow up and down the kill.  If you can't mow backwards, find another route to the top of the hill after you drive down it.

I have a steep front yard. It has five sets of seven granite steps with a four foot grass landing between each set of steps. It is pretty steep.

Because it is a sunny location, I have purposely planted something gardeners hate...crownveitch. it chokes out weeds and spreads to bloom pretty lavender pink flowers and it is deer resistent. It can be invasive and that is good for steep slopes as it prevents erosion.  Close to the steps, I planted several varieties of sedum. You can purchase a tray of sedum from Home Depot or Lowes (sorry, I forgot where I got mine). The sedum comes in a tray that you cut like a tray of brownies and plant about 12 inches apart. I did that two years ago and now I have an endless "carpet" of lovely sedum that is currently blooming as it prevents weed growth.

You CAN mow with a riding lawn mower, or a tractor, as long as you remember to mow STRAIGHT UP and STRAIGHT DOWN, and NEVER across the face of the hill. The reason you mow up and down is to prevent your machine from flipping over on you. It is NEVER SAFE, nor is it SMART, to mow across the face of any slope with a machine of any kind.

Your tractor should have enough power to get to the top of the hill.

45 degrees?  Get a square piece of paper.  Now fold it so you have a triangle.   That is 45 degrees.  You ain't that steep are you? That is more a cliff face.  You only can cut it driving DOWN HILL every time.  Or use a Weed Wacker. Or sheep.

Depending on how steep, you can mow by going straight up and down. Do not go across the slope.  If it is too steep, I would suggest using a string trimmer.  Good luck

self- propeled

Municipal mowers by Steiner (and other companies) offer some models that can mow steeper angles. However, they ain't cheap.

45 degrees!!! you could not walk up it ..and 5 acres ???..mmm...that would take days with a hand mower ..strim it 

Get some sheep, cows, goats, geese and have them mow the lawn by eating the grass. 

If you don’t have to bag the grass, use a weed wacker.